partial_duplication_graph

partial_duplication_graph(N, n, p, q, seed=None, *, create_using=None)

Returns a random graph using the partial duplication model.

Parameters:

Nint

The total number of nodes in the final graph.

nint

The number of nodes in the initial clique.

pfloat

The probability of joining each neighbor of a node to the duplicate node. Must be a number in the between zero and one, inclusive.

qfloat

The probability of joining the source node to the duplicate node. Must be a number in the between zero and one, inclusive.

seedinteger, random_state, or None (default)

Indicator of random number generation state. See Randomness.

create_usingGraph constructor, optional (default=nx.Graph)

Graph type to create. If graph instance, then cleared before populated. Multigraph and directed types are not supported and raise a NetworkXError.

Notes

A graph of nodes is grown by creating a fully connected graph of size n. The following procedure is then repeated until a total of N nodes have been reached.

1. A random node, u, is picked and a new node, v, is created.

2. For each neighbor of u an edge from the neighbor to v is created with probability p.

3. An edge from u to v is created with probability q.

This algorithm appears in [1].

This implementation allows the possibility of generating disconnected graphs.

References

[1]

Knudsen Michael, and Carsten Wiuf. “A Markov chain approach to randomly grown graphs.” Journal of Applied Mathematics 2008. <https://doi.org/10.1155/2008/190836>